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Relations among the Riemann Zeta and Hurwitz Zeta Functions, as Well as Their Products
, 2019 In this paper, several relations are obtained among the Riemann zeta and Hurwitz zeta functions, as well as their products. A particular case of these relations give rise to a simple re-derivation of the important results of Katsurada and Matsumoto on ...
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Mean Value Properties of the Hurwitz Zeta-Function.
MATHEMATICA SCANDINAVICA, 1992 Let \(\zeta^* (s,x) = \zeta (s,x + 1)\), where \(\zeta (s,a)\) \((0 < a \leq 1)\) is the Hurwitz zeta-function. The author proves that \[ \int^ 1_ 0 \left | \zeta^* \Bigl( {1 \over 2} + it, x \Bigr) \right |^ 2 dx = \log \left( {t \over 2 \pi} \right) + \gamma - 2 \text{Re} {\zeta (1/2 + it) \over 1/2 + it} + O \left( {1 \over t} \right), \] where ...
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On the Hurwitz zeta function of imaginary second argument [PDF]
Journal of Mathematical Physics, 2011 In this work, we exploit Jonquière's formula relating the Hurwitz zeta function to a linear combination of polylogarithmic functions in order to evaluate the real and imaginary part of ζH(s, ia) and its first derivative with respect to the first argument s.
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Functional equation for the periodic hurwitz zeta-function.
, 2016 Functional equation for the periodic Hurwitz zeta ...
Dabužinskas, Dominykas,
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On joint universality of the Riemann zeta-function and Hurwitz zeta-functions
, 2012 We construct classes of composite functions of the Riemann zeta-function and Hurwitz zeta function with transcendental parameter which are universal in the sense that their shifts uniformly on compact subsets of some region approximate any analytic ...
Laurinčikas, Antanas
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Contributions to the theory of the Hurwitz zeta-function
, 2007 International audienceWe give various contributions to the theory of Hurwitz zeta-function. An elementary part is the argument relating to the partial sum of the defining Dirichlet series for it; how much can we retrieve the whole from the part.
Tsukada, H +3 more
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On Generalized Hurwitz-Lerch Zeta Distributions
, 2009 In this paper, we introduce a function which is an extension to the general Hurwitz-Lerch Zeta function. Having defined the incomplete generalized beta type-2 and incomplete generalized gamma functions, some differentiation formulae are established for ...
Jain, Kumkum +2 more
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A random variable related to the Hurwitz zeta-function with algebraic parameter
, 2022 In this paper, we introduce a certain random variable closely related to the value-distribution of the Hurwitz zeta-function with algebraic parameter. We prove a version of the limit theorem, where the limit measure is presented by the law of this random
Mine, Masahiro
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Higher Derivatives of the Hurwitz Zeta Function
, 2011 The Riemann zeta function ζ(s) is one of the most fundamental functions in number theory. Euler demonstrated that ζ(s) is closely connected to the prime numbers and Riemann gave proofs of the basic analytic properties of the zeta function.
Musser, Jason
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A Mixture Model of Truncated Zeta Distributions with Applications to Scientific Collaboration Networks. [PDF]
Entropy (Basel), 2021 Jung H, Phoa FKH.
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